Set White difficult problems to solve at the board
One of the sharpest lines to meet 1 d4 is the Modern Benoni (1 d4 Nf6 2 c4 c5 3 d5 e6 4 Nc3 exd5 5 cxd5 d6). The hallmark of this opening is that Black makes the positional concession of allowing White a central majority and in return hopes for counterchances via active piece play. However, there are many other weird and wonderful ways to handle these "Benoni structures" as the very experienced chess coach and author Andrew Martin demonstrates in this highly engaging book.
Martin introduces the reader to (amongst others) the Vulture (1 d4 Nf6 2 c4 c5 3 d5 Ne4), the Clarendon Court (1 d4 c5 2 d5 f5) and the Snake Benoni (1 d4 Nf6 2 c4 c5 3 d5 e6 4 Nc3 exd5 5 cxd5 Bd6!?). All of these are outlandish tries but nevertheless set White difficult problems to solve at the board.
In other systems Black plays "Nimzo-style" and jettisons the dark-squared bishop in order to inflict weaknesses on the white pawn structure. One typical line is 1 d4 g6 2 c4 Bg7 3 Nc3 c5 4 d5 and now 4 ... Bxc3+!? 5 bxc3. This is a line favoured by elite grandmaster Hikaru Nakamura who has used it frequently in blitz and rapid chess. An advantage of playing this way is that it will usually take well booked up White players outside their comfort zone and force them onto their own resources.
If you want to inject a big dose of dynamism into your play with Black, the create some mayhem in the Benoni.